The prior art teaches processes and devices for determining the mass flow-rate of a fluid flowing inside a duct or pipe being angularly rotated in a reciprocating manner. The twisting moment generated by the Coriolis forces are then measured. The earliest devices for mass flow-rate measurement based on the measurement of Coriolis forces were of the gyroscopic type.
The first device the present invention can be more directly related to was patented in 1964 by A. J. Sipin (U.S. Pat. No. 3,355,944 issued in 1969), and consists of a "U" shaped pipe which is reciprocated about the axis of the inlet and outlet ends of the pipe. The pipe is provided with strain-gauge type means for measuring the deflections caused by the Coriolis forces.
The aforementioned reciprocating movement is caused by a motor and an electromagnet, and the amplitude of the oscillations is controlled (cfr. claim 5) by controlling the average amplitude of two speed signals obtained from two electromagnetic sensors provided along the sides of the "U". The flow-rate measurement is derived form the difference between these two signals. This patent also claims (see specifically claim 10) that the oscillation frequency is the resonant frequency of the system.
In 1964 the same A. J. Sipin patented (U.S. Pat. No. 3,329,019, issued in 1967) a similar device using completely rectilinear pipe geometry. The device was made to oscillate laterally by the same means, and with the same amplitude control as that in the prior case, i.e., two speed sensors located on opposite sides of the pipe, relative to the middle point of the pipe. This embodiment was also intended to operate at the resonance frequency of the system (see claim 6).
Among the reasons why the foregoing devices did not function in practice are the extremely low values (relative to the impulse forces applied to make the pipes oscillate,) of the Coriolis forces, the relevant deformations, and the frictional forces inherent in the mechanisms and the couplings. Additionally, deriving the flow-rate value from the difference between two speed signals is inexact. In fact, the flow-rate value can only be correctly deduced from the phase difference between the two speed signals whose amplitude remains constant for all normal conditions, except for the very special condition which is the object of the present invention.
At the flexural resonance frequency the flexural impulse force applied to the pipe produces a shift of the pipe in quadrature relative to the same force; on the other hand, the Coriolis force, always in quadrature relative to this flexural shift, produces, in turn, a twisting shift in the tube which is in phase with the same force, and whose oscillation frequency is lower than the twisting resonance frequency, and is therefore in quadrature relative to the twisting shift of the pipe. The end shift of the pipe, which is the vector sum of the two shifts in quadrature relative to each other, will therefore show, relative to the twisting shift of the pipe, a phase difference which must be considered when measuring the mass flow-rate.
In order to avoid the above-said functional limitations, variations were developed which led to the realization of commercial products.
The first patent which supplies a solution for Sipin's concept is the Cox patent (U.S. Pat. No. 4,127,028, issued in 1978), which recognized that the value of the mass flow-rate is related to the phase delay between the two signals obtained from the two sensors, rather than the difference in their amplitude (see FIG. 2 of the Cox patent). Cox also increased the signal/noise ratio by giving the pipe a racket shape so as to decrease its twisting stiffness. This reduced twisting stiffness lowered the twisting resonance frequency until it approached the flexural resonance frequency. Because of this small Coriolis forces could generate large deformations. Cox also coupled two matching pipes which were both parts of a single flow path, and made them vibrate in mutually opposite modes. This prevented vibrations from disturbing the device's supports, reduced the vibration energy, and by doubling the signal's amplitude improved the measuring precision, and rendered the system less sensitive to external vibrations.
A shortcoming of the Cox device is that although by shifting the twisting resonance frequency toward or to the inherent flexural (longitudinal) resonance fequency the system's frequency of oscillation approaches the twisting resonance frequency, an increase in sensitivity can be obtained, but the relationship between the phase displacement angles, and the Coriolis forces will no longer be linear.
Under these conditions, both small Coriolis forces, and small asymmetries cause increasingly large twisting oscillations, the effect of which is to magnify the Coriolis forces. Additionally, equilibrium under resonance conditions is achieved with the dispersion of energy through air friction, which varies as a function of the shifts according to a square law, and also through mechanical pipe deformation in hysteresis cycles, which makes fatigue breakage possible.
Beside the present non-linearity under conditions of twisting resonance, a phase shift also occurs between the motion and the generation of Coriolis forces. In fact, the twisting deformations caused by the Coriolis forces, which themselves are in phase with these forces, shift in phase to reach a phase advance of 90.degree.. Thus, the amplitudes of the two signals become different, and their phase delay decreases down to zero. Inasmuch as Cox uses for his signal the phase difference between the two equal amplitude movements of the position sensors installed on the pipes, (FIG. 2 of the patent,) it is clear that Cox' device will vibrate at frequencies which are relatively far from the device's twisting resonance frequency, and therefore cannot take advantage of extremely high amplification possible when operating at the twisting resonance frequency.
Another practical embodiment disclosed in U.S. Pat. No. 4,187,721, issued in 1980 to James E. Smith, improves the invention disclosed by Sipin.
In his patent, Smith recognizes the desirability of making a U-shaped pipe operate exactly and only at the flexural resonance frequency, since at this frequency the driving force needed to oscillate the pipe is small and will not interfere with the extremely small Coriolis forces. Furthermore, Smith, states that the flexural resonance frequency must be lower than the twisting resonance frequency in order to prevent the aforementioned operating anomalies, described above in connection with the Cox patent, from occuring.
With the improvement disclosed by Smith the measured signal becomes a highly linear function of the flow-rate, but another limitation remains. The signals which have to be processed are of infinitesimal magnitude, and to process them requires extremely sophisticated electronics. There are related problems with the stability of measured values for very low flow-rates, and with seismic-type disturbances.